How can a f-curve be used in an animation in BGE?
F-curve is generally used for controlling actions, I assume that you were asking "how to use action in BGE".

The simplest way is to set the Actuator type to Action. Then choose the action you want, and tweak a few settings within it, as shown below. Hope I didn't misunderstand that.





EDIT: I'm feeling that I sort of misunderstood that, did I? :-\